Reduced hierarchy equations of motion approach with Drude plus brownian spectral distribution: probing electron transfer processes by means of two-dimensional correlation spectroscopy.

We theoretically investigate an electron transfer (ET) process in a dissipative environment by means of two-dimensional (2D) correlation spectroscopy. We extend the reduced hierarchy equations of motion approach to include both overdamped Drude and underdamped brownian modes. While the overdamped mode describes the inhomogeneity of a system in the slow modulation limit, the underdamped mode expresses the primary vibrational mode coupled with the electronic states. We outline a procedure for calculating 2D correlation spectrum that incorporates the ET processes. The present approach has the capability of dealing with system-bath coherence under an external perturbation, which is important to calculate nonlinear response functions for non-markovian noise. The calculated 2D spectrum exhibits the effects of the ET processes through the presence of ET transition peaks along the Ω(1) axis, as well as the decay of echo signals.